tugas mtk 3

1. TUGAS 3
NAMA KELOMPOK : 1.SUSANDI 2.RAFIS 3.GERIAN
KELAS : 1EA
LATIHAN 7.1
1. ∫ 100 𝑑𝑥 = 100𝑥 + 𝑐
2. ∫ 6𝑥 𝑑𝑥 = 3𝑥2
+ 𝑐
3. ∫( 3𝑥2
+ 4𝑥 − 5) 𝑑𝑥 = 𝑥3
+ 2𝑥 −
5𝑥 + 𝑐
4. ∫( 𝑥2
+ 1)√ 𝑥 𝑑𝑥 =
2
7
𝑥2
1
+
2
3
𝑥2
3
+ 𝑐
5. ∫( 𝑥 𝑒
+ 𝑒 𝑥 ) 𝑑𝑥 =
𝑥 𝑒+1
𝑒+1
+ 𝑒 𝑥
+ 𝑐
6. ∫(10𝑥 + 30)3
10 𝑑𝑥 =
(10𝑥+30)4
4
+ 𝑐
7. ∫(𝑥2
− 3)4
2𝑥 𝑑𝑥 =
(𝑥2−3)5
5
+ 𝑐
8. ∫(𝑠𝑖𝑛2
𝑥cos 𝑥) 𝑑𝑥 =
𝑠𝑖𝑛3
3
𝑥 + 𝑐
9. ∫ 𝑥2
− 𝑠𝑖𝑛 𝑥3
𝑑𝑥 =
− cos 𝑥3
3
+ 𝑐
10. ∫ 𝐼𝑛 𝑥 𝑑𝑥 = 𝑥 𝐼𝑛 𝑥 = 𝑥 𝐼𝑛 𝑥 − 𝑥 +
𝑐
penyelesaian :
1. =
𝑑
𝑑𝑥
(100𝑥 + 𝑐) = 100𝑥 + 𝑐
2. =
𝑑
𝑑𝑥
(3𝑥2
+ 𝑐) = 6𝑥 + 0 = 100
3. =
𝑑
𝑑𝑥
(𝑥3
+ 2𝑥2
− 5𝑥 + 𝑐) = 3𝑥2
+ 4𝑥 − 5 + 0 = 3𝑥2
+4x-5
4. =
𝑑
𝑑𝑥
(
2𝑥
1
2
7
+
2𝑥
3
2
3
+ c)=
2𝑥
−1
2
14
+
6𝑥
1
2
6
+ 0 =
1𝑥
−1
2
7
+ 𝑥
1
2
5. =
𝑑
𝑑𝑥
(
𝑥 𝑒+1
𝑒+1
+ 𝑒 𝑥
+ 𝑐) =
𝑒+1.𝑥 𝑒+1−1
1𝑒1−1+0
+ 𝑥𝑒 𝑥−1
+ 𝑐 =
𝑒+𝑥 𝑒
1
+ 𝑥𝑒 𝑥−1
+ 0 = 𝑒 + 𝑥 𝑒
+
𝑥𝑒 𝑥−1
6. =
𝑑
𝑑𝑥
(10𝑥+30)4
4
+ 𝑐 =
10𝑥4
4
+
304
4
+ 𝑐 =
40𝑥3
4
+ 0 = 10𝑥3
7. =
𝑑
𝑑𝑥
(𝑥2−3)5
5
+ c =
𝑥10
5
−
35
5
+ 𝑐 =
10𝑥9
5
+ 0 = 2𝑥9
8. =
𝑑
𝑑𝑥
(
𝑠𝑖𝑛3
3
𝑥 + 𝑐) =
𝑠𝑖𝑛2 𝑥
3
.
sin 𝑥
3
+ 0 =
(1−𝑐𝑜𝑠2 𝑥) .
3
sin 𝑥
3
9. =
𝑑
𝑑𝑥
(
− cos 𝑥3
3
+ 𝑐) =
−3 sin 𝑥2
3
+ 0 = −sin 𝑥2
10. =
𝑑
𝑑𝑥
( 𝑥 𝐼𝑛 𝑥 − 𝑥 + 𝑐) = 𝑥.
𝑑𝑥
𝑥
− 1 =
𝑥−1𝑑𝑥
𝑥

2. LATIHAN 7.2
1. ∫8 𝑑𝑥
2. ∫
3
4
𝑑𝑥
3. ∫9.75 𝑑𝑥
4. ∫√3𝑑𝑥
5. ∫(
√40
3
√10+15
)𝑑𝑥
6. ∫16 √2 𝑑𝑡
7. ∫ 𝑒2
𝑑𝑥
8. ∫2𝜋 𝑑𝑟
9. ∫−21𝑑𝑢
10.∫
6
𝑒
𝑑𝑥
Penyelesaian :
1. = 8x+c
2. =
3
4
𝑥 + 𝑐
3. = 9𝑥. 75𝑥 + 𝑐
4. = √3 x+c
5. =
40𝑥
2
3
10𝑥
1
2+15𝑥
+ 𝑐
6. = 16𝑡. √2 𝑡 + c
7. = 𝑒𝑥2
+ c
8. = 2𝑟. 𝜋𝑟 + c
9. = -21 u + c
10.=
6𝑥
𝑒𝑥
+ c

3. LATIHAN 7.3
1. ∫ 𝑥5
𝑑𝑥
2. ∫ √ 𝑥34
𝑑𝑥
3. ∫ 𝑥√2
𝑑𝑥
4. ∫
1
𝑥2
𝑑𝑥
5. ∫ 𝑡100
𝑑𝑡
6. ∫ 𝑢2𝜋
𝑑𝑢
7. ∫
1
√𝑥
𝑑𝑥
8. ∫
𝑥5
𝑥2
𝑑𝑥
9. ∫ 𝑟−1
𝑑𝑟
10.∫
1
𝑡
𝑑𝑡
Penyelesaian :
1. =
𝑥6
6
+ 𝑐
2. = ∫ 𝑥
3
4 𝑑𝑥 =
𝑥
7
4
7
4
+ c =
4𝑥
7
4
7
+ 𝑐
3. =
𝑥√2+1
√2+1
+ 𝑐
4. =∫ 𝑥−2
𝑑𝑥 =
𝑥−1
−1
+ 𝑐 = −
1
𝑥
+ 𝑐
5. =
𝑡101
101
+ 𝑐
6. =
42𝜋+1
2𝜋+1
+ 𝑐
7. = ∫ 𝑥
−1
2 𝑑𝑥 =
𝑥
1
2
1
2
+ 𝑐 =
2𝑥
1
2
1
+ 𝑐
8. =
𝑥6
𝑥3
+ 𝑐
9. =
𝑟−1+1
−1+1
+ 𝑐 = ∞

4. 10.∫ 𝑡−1
𝑑𝑡 =
𝑡−1+1
−1+1
+ 𝑐 = ∞
LATIHAN 7.4
1. ∫ 𝑒 𝑡
𝑑𝑡
2. ∫ 𝑒20𝑥
𝑑𝑥
3. ∫ 𝑒 𝜋𝑥
𝑑𝑥
4. ∫ 𝑒0,25𝑥
𝑑𝑥
5. ∫ 𝑒
𝑥
5 𝑑𝑥
6. ∫ 𝑒√3𝑥
𝑑𝑥
7. ∫4 𝑥
𝑑𝑥
8. ∫23𝑥
𝑑𝑥
9. ∫1000,25𝑥
𝑑𝑥
10.∫ 𝜋
𝑥
5 𝑑𝑥
Penyelesaian :
1. = 𝑒 𝑡
+ 𝑐
2. =
1
20
𝑒20𝑥
+ 𝑐 =
𝑒20𝑥
5
+ 𝑐
3. =
1
𝜋
𝑒 𝜋𝑥
+ 𝑐 =
𝑒 𝜋𝑥
𝜋
+ 𝑐
4. =
1
0,25
𝑒0,25𝑥
+ 𝑐 =
𝑒0,25𝑥
0,25
+ 𝑐
5. =
1
𝑥
5
𝑒
𝑥
5 + 𝑐 =
5
𝑥
𝑒
𝑥
5 + 𝑐
6. =
1
√3
𝑒√3𝑥
+ 𝑐 =
𝑒√3𝑥
√3
+ c
7. =
1
𝐼𝑛 4
4 𝑥
+ 𝑐 =
4 𝑥
𝐼𝑛 4
+ 𝑐
8. =
1
3 𝐼𝑛 2
23𝑥
+ 𝑐 =
23𝑥
3 𝐼𝑛 2
+ 𝑐
9. =
1
0,25 𝐼𝑛 100
1000,25𝑥
+ 𝑐 =
1000,25𝑥
0,25 𝐼𝑛 100
+ 𝑐
10.=
1
𝑥
5
𝜋
𝑥
5 + 𝑐 =
5
𝑥
𝜋
𝑥
5 + 𝑐

5. LATIHAN 7.5
1. ∫cos 𝑣 𝑑𝑣
2. ∫sin(
1
2
𝜋𝑥)𝑑𝑥
3. ∫cos(18) 𝑑𝑥
4. ∫ 𝑠𝑒𝑐2
(√3𝑥)𝑑𝑥
5. ∫ 𝑐𝑠𝑐2
(2,5) 𝑑𝑥
6. ∫sec (
5
6
𝑥)tan(
5
6
𝑥)𝑑𝑥
7. ∫csc
x
3
𝑐𝑜𝑡
𝑥
3
𝑑𝑥
8. ∫csc(ex) cot(𝑒𝑥)𝑑𝑥
9. ∫sin 3𝜃 𝑑𝜃
10.∫cos(25𝜋𝑥) 𝑑𝑥
Penyelesaian :
1. = Sin v + c
2. = −
1
1
2𝜋
cos (
1
2
𝜋𝑥) + 𝑐 = −2𝜋cos (
1
2
𝜋𝑥) + 𝑐
3. =
1
8
sin(18𝑥) + 𝑐
4. =
1
√3
tan(√3𝑥) + 𝑐 =
tan(√3𝑥)
√3
+ 𝑐
5. = −
1
2,5
cot(2,5 𝑥) + 𝑐 =
−cot(2,5𝑥)
2,5
+ 𝑐
6. =
1
5
6
sec(
5
6
𝑥) + 𝑐 =
6
5
sec (
5
6
𝑥) + 𝑐
7. =
1
1
3
csc(
x
3
) + c = 3 csc (
𝑥
3
) + 𝑐
8. = −
1
𝑒
csc (ex) + c =
− csc( 𝑒𝑥)
𝑒
+ 𝑐
9. = −
1
3
cos(3𝜃) + 𝑐 =
−cos(3𝜃)
3
+ c
10.=
1
25𝜋
sin(25𝜋𝑥) + 𝑐 =
sin(25 𝜋𝑥)
25𝜋
+ c

6. LATIHAN 7.6
1. ∫
1
1+𝜃2
𝑑𝜃
2. ∫
𝑑𝑥
√16−𝑥2
3. ∫
1
49+𝑥2
𝑑𝑥
4. ∫
𝑑𝑡
0,25+𝑡2
5. ∫
𝑑𝑢
√𝑢2(𝑢2−1)
6. ∫
1
|𝑥|√𝑥2−41
𝑑𝑥
7. ∫
1
√
81
100
−𝑥2
𝑑𝑥
8. ∫
1
𝜋2+𝑥2
𝑑𝑥
9. ∫
𝑑𝑡
√𝑡2(𝑡2−
1
4
)
10.∫
1
|𝑥|√𝑥2−7
𝑑𝑥
Penyelesaian :
1. = 𝑡𝑎𝑛−1
𝜃 + 𝑐 = −𝑐𝑜𝑡−1
𝜃 + 𝑐
2. = ∫
1
√42−√𝑥2
𝑑𝑥 = 𝑠𝑖𝑛−1
(
𝑥
4
) + 𝑐
3. = ∫
1
√492+𝑥2
𝑑𝑥 =
1
√49
𝑡𝑎𝑛−1
(
𝑥
√49
) + 𝑐
4. = ∫
1
√0,252+𝑡2
𝑑𝑡 =
1
√0,25
𝑡𝑎𝑛−1
(
𝑡
√0,25
)+ 𝑐
5. = ∫
1
|𝑢|√𝑢2−√12
𝑑𝑢 =
1
1
𝑠𝑒𝑐−1
(
𝑢
1
) + 𝑐 = 𝑠𝑒𝑐−1( 𝑢) + 𝑐
6. = 𝑠𝑒𝑐−1
(
𝑥
41
) + c = - 𝑐𝑠𝑐−1
(
𝑥
41
) + c
7. = ∫
1
√
(9)2
10
−𝑥2
𝑑𝑥 = 𝑠𝑖𝑛−1
(
𝑥
9
10
) + 𝑐 =𝑠𝑖𝑛−1
(
10𝑥
9
) + 𝑐 = −𝑐𝑜𝑠−1
(
10𝑥
9
) + 𝑐
8.
1
𝜋
𝑡𝑎𝑛−1 𝑥
𝜋
+ 𝑐 = −
1
𝜋
𝑐𝑜𝑡−1
(
𝑥
𝜋
)+c

7. 9.= ∫
1
| 𝑡|√ 𝑡2−
(1)
2
2
𝑑𝑥 =
1
1
2
𝑠𝑒𝑐−1
(
𝑡
1
2
) + 𝑐 = 2𝑠𝑒𝑐−1(2𝑡) + 𝑐
10.𝑠𝑒𝑐−1
(
𝑥
7
) + 𝑐 = −𝑐𝑠𝑐−1
(
𝑥
7
) + 𝑐